question_answer

How is the mutual inductance of a pair of coils affected when,

(i) separation between the coils is increased

(ii) the number of turns in each coil is increased

(iii) a thin iron sheet is placed between the two coils, other factors remaining the same?

Explain your answer in each case.

Answer:

(i) When the relative distance between the coil is increased, the leakage of flux increases which reduces the magnetic coupling of the coils. So, magnetic flux linked with all the turns decreases.

Therefore, mutual inductance will be decreased.

(ii) Mutual inductance (M) for a pair of coil is given by

\[M=\frac{{{\mu }_{0}}{{N}_{1}}{{N}_{2}}A}{l}\]

\[\Rightarrow \]   \[M\propto {{N}_{1}}{{N}_{2}}\]

Therefore, when the number of turns in each coil increases, the mutual inductance also increases.

(iii) Since, mutual inductance (M) is directly proportional to the relative permeability of space

\[{{\mu }_{r}}.\]

i.e.        \[M=\frac{{{\mu }_{0}}{{\mu }_{r}}{{N}_{1}}{{N}_{2}}A}{l}\]

Hence, mutual inductance (M) is increased on placing thin iron sheet between the two coils.